Uncertainty And Vagueness In Knowledge Based Systems

The primary aim of this monograph is to provide a formal framework for the representation and management of uncertainty and vagueness in the field of artificial intelligence. It puts particular emphasis on a thorough analysis of these phenomena and on the development of sound mathematical modeling approaches. Beyond this theoretical basis the scope of the book includes also implementational aspects and a valuation of existing models and systems. The fundamental ambition of this book is to show that vagueness and un certainty can be handled adequately by using measure-theoretic methods. The presentation of applicable knowledge representation formalisms and reasoning algorithms substantiates the claim that efficiency requirements do not necessar ily require renunciation of an uncompromising mathematical modeling. These results are used to evaluate systems based on probabilistic methods as well as on non-standard concepts such as certainty factors, fuzzy sets or belief functions. The book is intended to be self-contained and addresses researchers and practioneers in the field of knowledge based systems. It is in particular suit able as a textbook for graduate-level students in AI, operations research and applied probability. A solid mathematical background is necessary for reading this book. Essential parts of the material have been the subject of courses given by the first author for students of computer science and mathematics held since 1984 at the University in Braunschweig.

The ideas of uncertain variables based on uncertain logics have been introduced and developed for a wide class of uncertain systems. The purpose of this mo- graph is to present basic concepts, definitions and results concerning the uncertain variables and their applications to analysis and decision problems in uncertain systems described by traditional mathematical models and by knowledge rep- sentations. I hope that the book can be useful for graduate students, researchers and all readers working in the field of control and information science. Especially for those interested in the problems of uncertain decision support systems and unc- tain control systems. I wish to express my gratitude to my co-workers from the Institute of Control and Systems Engineering of Wroclaw University of Technology, who assisted in the preparation of the manuscript. My special thanks go to Dr L.Siwek for the valuable remarks and for his work concerning the formatting of the text.

A variety of formalisms have been developed to address such aspects of handling imperfect knowledge as uncertainty, vagueness, imprecision, incompleteness, and partial inconsistency. Some of the most familiar approaches in this research field are nonmonotonic logics, modal logics, probability theory (Bayesian and non-Bayesian), belief function theory, and fuzzy sets and possibility theory. ESPRIT Basic Research Action 3085, entitled Defeasible Reasoning and Uncertainty Management Systems (DRUMS), aims to contribute to the elucidation of similarities and differences between these formalisms. It consists of 11 active European research groups. The European Conference on Symbolic and Quantitative Approaches to Uncertainty (ESQAU) provides a forum for these groups to meet and discuss their scientific results. This volume contains 42 contributions accepted for the ESQAU meeting held in October 1991 in Marseille, together with 12 articles presenting the activities of the DRUMS groups and two invited presentations.

As we stand at the precipice of the twenty first century the ability to capture and transmit copious amounts of information is clearly a defining feature of the human race. In order to increase the value of this vast supply of information we must develop means for effectively processing it. Newly emerging disciplines such as Information Engineering and Soft Computing are being developed in order to provide the tools required. Conferences such as the International Conference on Information Processing and ManagementofUncertainty in Knowledge-based Systems (IPMU) are being held to provide forums in which researchers can discuss the latest developments. The recent IPMU conference held at La Sorbonne in Paris brought together some of the world's leading experts in uncertainty and information fusion. In this volume we have included a selection ofpapers from this conference. What should be clear from looking at this volume is the number of different ways that are available for representing uncertain information. This variety in representational frameworks is a manifestation of the different types of uncertainty that appear in the information available to the users. Perhaps, the representation with the longest history is probability theory. This representation is best at addressing the uncertainty associated with the occurrence of different values for similar variables. This uncertainty is often described as randomness. Rough sets can be seen as a type of uncertainty that can deal effectively with lack of specificity, it is a powerful tool for manipulating granular information.

A unified and systematic description of analysis and decision problems within a wide class of uncertain systems, described by traditional mathematical methods and by relational knowledge representations. Prof. Bubnicki takes a unique approach to stability and stabilization of uncertain systems.

This five-volume set clearly manifests the great significance of these key technologies for the new economies of the new millennium. The discussions provide a wealth of practical ideas intended to foster innovation in thought and, consequently, in the further development of technology. Together, they comprise a significant and uniquely comprehensive reference source for research workers, practitioners, computer scientists, academics, students, and others on the international scene for years to come.